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How can i find the end behavior with these two functions?

 

 Oct 3, 2017
 #1
avatar+8079 
+1

How can i find the end behavior with these two functions?

 

\(f(x)=\frac{-6x}{3x-5}\\ f(x)=x^2-4x-5\)

 

\(\frac{-6x}{3x-5}=x^2-4x-5 \)

\(-6x=(x^2-4x-5)\times (3x-5)\\ -6x=3x^3-5x^2-12x^2+20x-15x+25\\ \color{blue}3x^3-17x^2+11x+25=0\)

 

\(x_1 \approx-.88231\\ x_2\approx 2.1443\\ x_3 \approx 4.4041\\ WOLFRAM\ |\ ALPHA\)

 

laugh  !

 Oct 3, 2017
 #2
avatar+99350 
+1

Mmm I do not think that is what the guest wanted asinus :)

 

\(f(x)=\frac{-6x}{3x-5}\)

 

This has an asymptote at 

3x-5=0

x=5/3

 

lim as x tends to 5/3 from above = - infinity

lim as x tends to 5/3 from below = + infinity

 

As x tends to +infinity  y tends to -2

As x tends to -infinity  y tends to -2

 

Here is the graph.

 

 Oct 3, 2017

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